Direct, Inverse, and Joint Variation Calculator

The calculator will find the constant of variation and other values for the direct, inverse (indirect), joint, and combined variation problems, with steps shown.

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Write here the 'find `k`' condition. For example, write x=3, y=5, z=15, if you are given "z=15, when x=3, y=5".

Write here the 'find variable' condition. For example, write y=2, z=10, if you are given "find x, when y=2, z=10".

If you don't need to find a variable, leave this field empty.

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Solution

Your input: find the constant of variation $$$k$$$ given $$$z=k \frac{x^{2}}{y}$$$, $$$z=7$$$ when $$$x=5$$$ and $$$y=3$$$ and find $$$y$$$ when $$$z=12$$$ and $$$x=1$$$.

We have that $$$z=k \frac{x^{2}}{y}$$$.

Plug in the given values to find $$$k$$$: $$$7=k \cdot \frac{5^{2}}{3^{1}}$$$.

Solving this equation, we obtain that $$$k=\frac{21}{25}$$$.

Now find $$$\mathtt{\text{y}}$$$.

Plug in the given values and found $$$k$$$ to find $$$y$$$: $$$12=\frac{21 \frac{1^{2}}{y^{1}}}{25}$$$.

From this equation, we have that $$$y=\frac{7}{100}$$$.

Answer: the constant of variation is $$$k=\frac{21}{25}$$$, $$$y=\frac{7}{100}$$$.